Electrical filters are used for a wide variety of purposes in virtually every type of electronic communication and control systems. In particular, bandpass filters are of great value in communication equipment in permitting passage of desired received signals in certain frequency ranges while attenuating noise and undesired signals in surrounding frequency ranges.
An ideal bandpass filter would be one which has uniform transmission (i.e. the amplitude characteristic) and uniform delay (i.e. linear phase) for all frequency components within the passband of the filter, while simultaneously exhibiting zero transmission outside of the passband. It has been theoretically shown to be impossible to achieve this in classical articles such as "Fourier Transforms in the Complex Domain" by Paley and Wiener in the Am. Math. Society Colloquia, Vol. XIX, Therorem 12, pages 16-18, 1934 and "The Physical Realizability and Realization of Linear Phase Networks" by P. M. Chirlian, Quart. Appl. Math., Vol. 18, pages 31-35, April 1960.
Although this ideal filter cannot be achieved, reasonably good approximations exist for obtaining bandpass characteristics (as well as low pass characteristics), and a great deal of research has been done to develop filters providing such approximations. This research has led to the development of such classic models as the Butterworth model (which seeks a maximally flat characteristic for either the phase or attenuation) and the Chebyshev model (which provides for an equal ripple of the characteristic under control between the limits of the passband).
During the early development of such approximations for bandpass filters, the primary concern was for the amplitude characteristic. This resulted from the fact that most of the applications for such bandpass filters involved speech transmission, and, in such speech transmission, phase distortion was not nearly as significant as amplitude distortion. In the approximations developed, the better the approximation of the amplitude characteristic, the greater the phase distortion turned out to be near the band edge. Similarly, improvements in the phase characteristic led to a deterioration of the amplitude characteristic until it resembled a Bell-shaped curve.
Accordingly, when it was necessary to have a reasonably good phase characteristic in addition to a good amplitude characteristic, it became typical design procedure to utilize a filter network providing the desired amplitude characteristics and known but unacceptable phase characteristics. This network is then followed by an all-pass equalizer to improve the overall phase characteristics. In this method, an equalization pole is typically required for each pole in the filter network. This conventional approach is generally considered a straightforward and acceptable method for implementation of high quality linear phase filters. The main objection to this method however is the large number of components required. This increases the time needed to adjust the filters, and the quality and training of the personnel needed to perform the alignment. However, since the original need for such techniques was not great, these difficulties were readily tolerated.
Eventually, with the development of high capacity communication systems, the phase characteristic became more important since vast amounts of data other than simple speech had to be handled by such systems. Under these conditions, phase distortion often became a serious problem. Correspondingly, interest heightened in providing a filter, and in particular a bandpass filter, which would have both good amplitude and good phase characteristics without the difficulties encountered in prior equalization techniques.
SAW type filters represent one recently developed type of filter which shows that it is possible to make close approximations to the ideal bandpass filter characteristics both for amplitude and phase. SAW filters, however, have certain features which make them very undesirable for use in wideband analog systems such as FM-FDM. The first is the large insertion loss. This necessitates high intercept point amplifiers to replace the system gain which is lost. Secondly, SAWs exhibit triple transient reflections, or echo, which limit the system's NPR. A third shortcoming of SAW filters is the temperature dependency of the narrow bandwidth units when fabricated in a lowcost material such as Lithium Niobate.
Another technique developed for achieving both a good amplitude characteristic and a relatively linear phase response is described in an article by Robert M. Lerner entitled "Bandpass Filters with Linear Phase", Proceedings of the IEEE, March 1964, pages 249-268. Essentially, this article describes full- and half-lattice filter systems with the delay self-equalized over a large portion of the filter 3-dB bandwidth. FIG. 2 illustrates the basic half-lattice filter envisioned by Lerner with a pair of lattice arms 10 and 12 coupled across a 1:1:1 transformer 14. The individual arms 10 and 12 are shown for an admittance configuration Y in FIG. 2. As taught by Lerner, in both cases, Y.sub.A and Y.sub.B consist of a number of (lossless) series resonant circuits connected in parallel to one another. The resonators are of two types; all but two are in-band resonators in which the inductances all have the same magnitude L; the other two are corrector resonators whose inductors are nominally 2L. The resonators are tuned to frequencies f.sub.1, f.sub.2 . . . at equal intervals 2 .DELTA.f across the desired passband, alternate frequencies f.sub.1, f.sub.3, f.sub.5 . . . being assigned to Y.sub.A and f.sub.2, f.sub.4 . . . being assigned to Y.sub.B. A frequency .DELTA.f below f.sub.1 is the nominal 6-dB band edge of the filter. One of the corrector resonators is tuned to this frequency and assigned to the network branch opposite to that of the f.sub.1 resonator (Y.sub.B in FIG. 2). Similarly, the other corrector resonator is tuned to a frequency .DELTA.f above that of the uppermost in-band resonator f.sub.n and assigned to the opposite network branch. The resistance R is taken equal to 4/.pi. times the (calculated) impedance of L at a frequency of 2 .DELTA.f Hz. In addition, Lerner taught that parallel-tuned LC (resonant in-band) and, in some cases, series-tuned LC circuits (resonant out-of-band) may be placed across the loads for compensation purposes.
FIG. 3 illustrates the output of Lerner's filter using nine poles. Although it is apparent that a reasonably linear phase is achieved across the majority of the passband, it is also clear that substantial deterioration, or so-called "ears" exist at the edges of the passband. Some improvement can be achieved by increasing the number of poles. But this is undesirable both from a cost and size viewpoint, as well as from the fact that substantial adjustment is necessary for a large number of poles.